A terminating decimal is a decimal that ends. For example 1/2 =0.5 is a terminating decimal, whereas 1/3 =0.333333... is a non-terminating decimal.

In the first statement, we know 3 is a factor in the denominator so we are always going to get non-terminating decimals. For example, 1/3 =0.3333.., 1/6 = 0.166666..., 1/9 = 0.1111111. We can narrow the choices down to A and D.

In the second statement x is narrowed down to 81, 27, 9 and 3. These are all numbers that have 3 as a factor and we just saw in statement one if the denominator has a factor of 3, it will always be a non-terminating decimal. So the answer is D.

Make sense?

Take care,
Sionainn Marcoux
BA - Stanford University, MPP - Harvard University
Instructor, tutor for Princeton Review and Airbnb host
In other words a blend of Jamie Escalante from Stand and Deliver, Julie from The Love Boat, and Schneider the Super from One Day at a Time.

VJesus12 wrote:If x is a positive integer greater than 1, is 1/x a terminating decimal?

1) x has 3 as a factor
2) x is a factor of 81

Target question: Is 1/x a terminating decimal?
This is a good candidate for rephrasing the target question.

There's a nice rule that says something like,
If a/b results in a terminating decimal, then the denominator, b, MUST be the product of 2's and 5's only!
So, for example, if b = 20, the fraction 1/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.

Given all of this, we can REPHRASE our target question as follows:
REPHRASED target question: Does the prime factorization of x consist of 2's and 5's only?

Statement 1: x has 3 as a factor
This means that 3 is in prime factorization of x
So, the answer to the REPHRASED target question is NO, the prime factorization of x does NOT consist of 2's and 5's only
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is a factor of 81
The positive factors of 81 are: 1, 3, 9, 27, 81
NONE of these factors is 2 or 5
So, the answer to the REPHRASED target question is NO, the prime factorization of x does NOT consist of 2's and 5's only
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent